A038389 Let f(n) be the smallest number such that the arithmetic mean (A) and geometric mean (G) of n and f(n) are both integers; sequence gives A values.

1, 2, 3, 4, 5, 6, 7, 5, 5, 10, 11, 12, 13, 14, 15, 10, 17, 10, 19, 20, 21, 22, 23, 15, 13, 26, 15, 28, 29, 30, 31, 17, 33, 34, 35, 20, 37, 38, 39, 25, 41, 42, 43, 44, 25, 46, 47, 30, 25, 26, 51, 52, 53, 30, 55, 35, 57, 58, 59, 60, 61, 62, 35, 34, 65, 66, 67, 68, 69, 70, 71, 37, 73, 74, 39, 76, 77, 78

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

It is the average of A038387 with n, both of which are multiplicative. - Christian G. Bower, May 16 2005

However, this sequence is not multiplicative. The first nonmultiplicative term is a(72) = 37 which is not multiplicative since a(8)*a(9) = 5*5 = 25. - Andrew Howroyd, Feb 12 2018

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A038387, A038388.

Programs

Mathematica

Table[k = 1; While[Nand @@ IntegerQ /@ {a = (n + k)/2, Sqrt[n*k]}, k++]; a, {n, 78}] (* Jayanta Basu, Jul 14 2013 *)

PARI

a(n)={for(k=1, n, if((n+k)%2==0 && issquare(n*k), return((n+k)/2)))} \\ Andrew Howroyd, Feb 12 2018